An approach for nonlinear change point analysis

We demonstrate an approach for assessing changes in nonlinear regression models for longitudinal data at alternative points in time. We use adaptive regression methods generating nonlinear models for means over time while accounting for autoregressive correlations. Power transforms of predictors are systematically added to models; then extraneous transforms, if any, are removed and powers of remaining transforms adjusted. Change points are assessed by considering transforms of unrestricted time and time restricted to after the change point. Alternative models are compared using likelihood cross-validation including the choice of change point. We conduct an example analysis of 11,603 CD4 counts measured semiannually from 1990 to 2002 for 1,058 HIV-positive white male participants of the Multicenter AIDS Cohort Study. Triple combination therapy and protease inhibitors became the standard of care in 1996, and so mean CD4 counts for HIV-positive patients are likely to change at about this point in time. This was supported. The selected model was distinctly nonlinear, changing in 1995 with mean CD4 counts decreasing from 416 in 1990 to 208 in mid-1995 and then increasing to 495 in 2002. This analysis demonstrates nonlinear regression change point modeling and the advantage of considering nonlinear curves in those analyses.